Let \(G\)  be a finite simple graph, one with no loops or multiple edges. The
set of vertices of \(G\)  is \(VG\)  and \(EG\)  is the set of edges. The order
of \(G\)  is \(p=\left|VG\right|\)  and the size is \(q=\left|EG\right|\) ; these notations will hold throughout. (For both basic
graph-theoretic concepts and topics in algebraic graph theory, see [1]}.) Edges are two-element subsets of \(VG\) . Instead of the conventional
notations \(\lbrace x,y\rbrace \)  or \(xy\)  for the edge with vertices \(x\)  and \(y\) , we write
\(\left[ x,y\right] \) , especially in the algebra frame-work where we see \(xy=\left[ x,y\right] \) . The vertices of an edge \([x,y]\)  are called adjacent, denoted \(x\sim y\) . Different edges are also called adjacent
when they share a vertex.
